Rational doubt ( doubt in rational number)

Asked Apr 30 '14 at 16:17

Active Apr 30 '14 at 16:23

Viewed 117 times

If there is a prime number x, if we reciprocate it we will get 1/x.

Reciprocal of prime number will be a rational number , Except 1/2 and 1/5 , every number which is reciprocal of prime number is a recurring non terminating decimal number.

Question- How to find that after how many digit recurring numbers will repeat ? How to find the recurring numbers?

edited Apr 30 '14 at 16:23

asked Apr 30 '14 at 16:17

Except 1/2 and 1/5 – Apr 30 '14 at 16:23
@MJD In above question link conditions are given . How to calculate without any condition ? Here in my question numerator is 1. So its different. – Apr 30 '14 at 16:29
The period $n$ in which $\frac1p$ repeats is the smallest $n$ such that $10^n-1$ is a multiple of $p$. For example, $10^6-1 = 999999$ is a multiple of $7$, but $10^5-1$ is not, so $\frac17$ repeats every 6 digits. However, no general rule is known that describes the smallest such $n$ in general. – MJD Apr 30 '14 at 16:29
(The question has come up here many times before; a search for “period of decimal” will produce many relevant answers.) – MJD Apr 30 '14 at 16:30
For example, there are three answers at Compute the period of a decimal number a priori – MJD Apr 30 '14 at 16:33

Rational doubt ( doubt in rational number)

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